Bring a pot of salted water to a boil for the potatoes. Add potatoes and simmer until fork-tender, about 15–20 minutes.

While the potatoes cook, pat chicken dry and season generously with salt, pepper, half the minced garlic, thyme, and rosemary. Let rest for 5 minutes.

Heat a large skillet over medium-high heat and add olive oil. When shimmering, place chicken skin-side down. Cook without moving until the skin is golden and crisp, about 6–8 minutes. Flip and add 1 tablespoon butter; baste the chicken with the melting butter and pan juices, cooking until an internal temperature of 165°F for breasts or 175°F for thighs.

Remove the chicken to a resting plate and tent with foil.

Pour off excess fat from the skillet, leaving a tablespoon. Add remaining butter and garlic, cook until fragrant and slightly golden. Spoon this garlic-herb butter over the resting chicken.

In a separate sauté pan, melt 1 tablespoon butter over medium heat. Add carrots and a pinch of salt. Sauté for 6–8 minutes until they start to soften. Add honey and apple cider vinegar, stirring until the carrots are glossy and caramelized, about 2 more minutes.

Mash the drained potatoes with warm milk, sour cream, and a knob of butter. Taste and season with salt and pepper. For extra silkiness, use a ricer or hand mixer on low for a few pulses.

Plate with a generous scoop of mashed potatoes, a golden piece of garlic herb chicken on top or beside, and a bright pile of glazed carrots. Finish with chopped parsley and an extra drizzle of herb butter if you have it left.